To say that software is math doesn't really tell the whole story, though. In this sense, the word "Math" is being used in two different ways. The "Math" that is discovered (and thus not patentable) is the kind that tells us things about orders of infinity, and the countability of natural numbers.

Computer Science 101: software is just multiple binaries (0 and 1) i.e. abstract in this case therefore part of math. For example, show a word processor, a music, a movie in palpable form without any medium.

Software is an arrangement of 0s and 1s; a car is just an arrangement of metal and rubber. I think the question should be: was the arrangement found, or built? Proper mathematics is found, but software is most definitely built.

Anything which requires an author or other type of artisan is "built". Why on earth should software alone be patentable, just because it uses math as its working medium?

"Software is an arrangement of 0s and 1s; a car is just an arrangement of metal and rubber. I think the question should be: was the arrangement found, or built? Proper mathematics is found, but software is most definitely built."

I don't agree with your distinction.

You may not be aware of this, but in computer science discrete mathematics courses, we do study how to apply mathematical concepts like induction towards computer algorithms.

If an algorithm is patented, and a developer can prove that the algorithm is mathematically derivable, then would you say the algorithm patent should be invalidated? It is sort of a trick question, since every algorithm is mathematically derivable, given adequate specification.

I'd go as far as to say a genuine distinction between mathematical and computer algorithms is blurred to the point of non-existence seeing as one can clearly be translated to the other (within physical constraints of the machine).

Could you elaborate on a fundamental difference?

Given the same problem, many developers will come up with overlapping algorithms. You may say "oh just use a different algorithm", but now developers are wasting their time in search for algorithms with less desirable properties in order to satisfy a patent holder's monopoly. Considering that many patent holders deliberately file dozens of variations on the same idea to deliberately block other implementations, it's no wonder honest developers are pissed off with software patents.